Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation

We present a simple numerical solution algorithm for a gradient flow for the Modica–Mortola functional and numerically investigate its dynamics. The proposed numerical algorithm involves both the operator splitting and the explicit Euler methods. A time step formula is derived from the stability ana...

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Autores principales:	Yibao Li, Sungha Yoon, Jian Wang, Jintae Park, Sangkwon Kim, Chaeyoung Lee, Hyundong Kim, Junseok Kim
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f0733653ddd848d58da255a6c456502a
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spelling	oai:doaj.org-article:f0733653ddd848d58da255a6c456502a2021-11-29T00:56:53ZFast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation1563-514710.1155/2021/2414209https://doaj.org/article/f0733653ddd848d58da255a6c456502a2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2414209https://doaj.org/toc/1563-5147We present a simple numerical solution algorithm for a gradient flow for the Modica–Mortola functional and numerically investigate its dynamics. The proposed numerical algorithm involves both the operator splitting and the explicit Euler methods. A time step formula is derived from the stability analysis, and the goodness of fit of transition width is tested. We perform various numerical experiments to investigate the property of the gradient flow equation, to verify the characteristics of our method in the image segmentation application, and to analyze the effect of parameters. In particular, we propose an initialization process based on target objects. Furthermore, we conduct comparison tests in order to check the performance of our proposed method.Yibao LiSungha YoonJian WangJintae ParkSangkwon KimChaeyoung LeeHyundong KimJunseok KimHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Yibao Li Sungha Yoon Jian Wang Jintae Park Sangkwon Kim Chaeyoung Lee Hyundong Kim Junseok Kim Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
description	We present a simple numerical solution algorithm for a gradient flow for the Modica–Mortola functional and numerically investigate its dynamics. The proposed numerical algorithm involves both the operator splitting and the explicit Euler methods. A time step formula is derived from the stability analysis, and the goodness of fit of transition width is tested. We perform various numerical experiments to investigate the property of the gradient flow equation, to verify the characteristics of our method in the image segmentation application, and to analyze the effect of parameters. In particular, we propose an initialization process based on target objects. Furthermore, we conduct comparison tests in order to check the performance of our proposed method.
format	article
author	Yibao Li Sungha Yoon Jian Wang Jintae Park Sangkwon Kim Chaeyoung Lee Hyundong Kim Junseok Kim
author_facet	Yibao Li Sungha Yoon Jian Wang Jintae Park Sangkwon Kim Chaeyoung Lee Hyundong Kim Junseok Kim
author_sort	Yibao Li
title	Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
title_short	Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
title_full	Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
title_fullStr	Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
title_full_unstemmed	Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation
title_sort	fast and efficient numerical finite difference method for multiphase image segmentation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/f0733653ddd848d58da255a6c456502a
work_keys_str_mv	AT yibaoli fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT sunghayoon fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT jianwang fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT jintaepark fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT sangkwonkim fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT chaeyounglee fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT hyundongkim fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation AT junseokkim fastandefficientnumericalfinitedifferencemethodformultiphaseimagesegmentation
_version_	1718407683965452288

Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation

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